David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Philosophical Logic 31 (2):181-196 (2002)
Two models of second-order ZFC need not be isomorphic to each other, but at least one is isomorphic to an initial segment of the other. The situation is subtler for impure set theory, but Vann McGee has recently proved a categoricity result for second-order ZFCU plus the axiom that the urelements form a set. Two models of this theory with the same universe of discourse need not be isomorphic to each other, but the pure sets of one are isomorphic to the pure sets of the other. This paper argues that similar results obtain for considerably weaker second-order axiomatizations of impure set theory that are in line with two different conceptions of set, the iterative conception and the limitation of size doctrine
|Keywords||categoricity second-order set theory iterative conception limitation of size|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
Gabriel Uzquiano (2009). Bad Company Generalized. Synthese 170 (3):331 - 347.
Similar books and articles
Mark F. Sharlow (1987). Proper Classes Via the Iterative Conception of Set. Journal of Symbolic Logic 52 (3):636-650.
B. Biró & S. Shelah (1988). Isomorphic but Not Lower Base-Isomorphic Cylindric Set Algebras. Journal of Symbolic Logic 53 (3):846-853.
Ignacio Jané & Gabriel Uzquiano (2004). Well- and Non-Well-Founded Fregean Extensions. Journal of Philosophical Logic 33 (5):437-465.
Christopher Menzel (1986). On the Iterative Explanation of the Paradoxes. Philosophical Studies 49 (1):37 - 61.
James Walmsley (2002). Categoricity and Indefinite Extensibility. Proceedings of the Aristotelian Society 102 (3):217–235.
James H. Schmerl (1980). Decidability and ℵ0-Categoricity of Theories of Partially Ordered Sets. Journal of Symbolic Logic 45 (3):585 - 611.
Agustin Rayo (1999). Toward a Theory of Second-Order Consequence. Notre Dame Journal of Formal Logic 40 (3):315-325.
Jouko Väänänen (2012). Second Order Logic or Set Theory? Bulletin of Symbolic Logic 18 (1):91-121.
Added to index2009-01-28
Total downloads32 ( #59,893 of 1,140,358 )
Recent downloads (6 months)2 ( #85,215 of 1,140,358 )
How can I increase my downloads?